Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles

Abstract

Eigenstates of local many-body interacting systems that are far from spectral edges are thought to be ergodic and close to being random states. This is consistent with the eigenstate thermalization hypothesis and volume-law scaling of entanglement. We point out that systematic departures from complete randomness are generically present in mid-spectrum eigenstates, and focus on the departure of the entanglement entropy from the random-state prediction. We show that the departure is (partly) due to spatial correlations and due to orthogonality to the eigenstates at the spectral edge, which imposes structure on the mid-spectrum eigenstates.

8 pages, 5 figures, 122 references + 6 pages, 9 figures in 8 Appendices

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• Entanglement of magnon excitations in spin chains
• Quantifying quantum chaos through microcanonical distributions of entanglement
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• Stable many-body localization under random continuous measurements in the no-click limit
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• Multifractality of many-body non-Hermitian skin effect
• Subsystem distances between quasiparticle excited states
• Finite-size scaling analysis of eigenstate thermalization
• Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
• Fermionic Magic Resources of Quantum Many-Body Systems
• Symmetry breaking in chaotic many-body quantum systems at finite temperature
• Typical entanglement entropy in systems with particle-number conservation
• Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
• Subsystem entropy in 2d CFT and KdV ETH
• Cat states carrying long-range correlations in the many-body localized phase
• Characterizing quantum chaoticity of kicked spin chains
• Quantum ergodicity and scrambling in quantum annealers
• Adding boundary terms to Anderson localized Hamiltonians leads to unbounded growth of entanglement
• Late-time ensembles of quantum states in quantum chaotic systems
• Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1/2$ chains
• Entanglement patterns of quantum chaotic Hamiltonians with a scalar U(1) charge
• Chaos and bi-partite entanglement between Bose-Joephson junctions
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Determining non-Hermitian parent Hamiltonian from a single eigenstate
• Universal entanglement entropy in the ground state of biased bipartite systems
• Deviation from maximal entanglement for mid-spectrum eigenstates of local Hamiltonians
• No eigenstate of the critical transverse-field Ising chain satisfies the area law
• Volume-law entanglement entropy of typical pure quantum states
• Excitations of Quantum Many-Body Systems via Purified Ensembles: A Unitary-Coupled-Cluster-based Approach
• Average mutual information for random fermionic Gaussian quantum states